A hearing took place Friday for William Balfour. He's charged in the October 2008 murders.
Balfour was married to the sister of the Oscar-winning actress and singer.
Prosecutors said the threats began in early 2008 when Balfour moved out of the family's home.
On the day of the murders, he reportedly became enraged when he went to the home and saw balloons that a new boyfriend had given Hudson's sister, Julia.